Question

Carbon-14 has a half-life of 5720 years and this is a first-order reaction. If a piece of wood has converted 11.5% of the carbon-14, then how old is it? 4290 years 2375 years 17160 years 4750 years 1008 years

Answer 1

Answer:

1008 years

Explanation:

Given that:

Half life = 5720 years

$t_{1/2}=\frac{\ln2}{k}$

Where, k is rate constant

So,  

$k=\frac{\ln2}{t_{1/2}}$

$k=\frac{\ln2}{5720}\ year^{-1}$

The rate constant, k = 0.00012 year⁻¹

Using integrated rate law for first order kinetics as:

$[A_t]=[A_0]e^{-kt}$

Where,  

$[A_t]$ is the concentration at time t

$[A_0]$ is the initial concentration

Given:

11.5 % is decomposed which means that 0.115 of $[A_0]$ is decomposed. So,

$\frac {[A_t]}{[A_0]}$ = 1 - 0.115 = 0.885

t = ?

$\frac {[A_t]}{[A_0]}=e^{-k\times t}$

$0.885=e^{-0.00012\times t}$

t = 1008 years